The \(\pm \)  option in (REF ) also appears in the b.c.s for higher spin fields (as in the AdS case [1]}, [2]}). Since \(a(\eta )\)  is odd under \(\eta \rightarrow -\eta \) , we can infer right choice for the tetrad: the conformal tetrad \(\tilde{e}^{\;\!a}_{\mu }\)  (with \(\eta _{ab}\tilde{e}^{\;\!a}_{\mu }\tilde{e}^{\;\!b}_{\nu }=\tilde{g}_{\mu \nu }\) ) satisfies a Neumann b.c. (or, equivalently, the symmetric condition \(\tilde{e}^{\;\!a}_{\mu }(\eta ,{\bf x})=\tilde{e}^{\;\!a}_{\mu }(-\eta ,{\bf x})\) ) while the physical tetrad \(e^{a}_{\mu }=a\tilde{e}^{\;\!a}_{\mu }\)  (with \(\eta _{ab}e^{a}_{\mu }e^{b}_{\nu }=g_{\mu \nu }\) ) satisfies a Dirichlet b.c. (or, equivalently, the anti-symmetric condition \(e^{a}_{\mu }(\eta ,{\bf x})=-e^{a}_{\mu }(-\eta ,{\bf x})\) ). As shown in [3]}, this condition successsfully explains: (i) the absence of primordial vector perturbations; (ii) the absence of primordial “decaying-mode" scalar and tensor perturbations (which synchronizes the scalar perturbations, explaining the observed oscillations in the CMB temperature spectrum and their phases); and (iii) the fact that bang seems to be a particularly mild singularity (a “Weyl singularity" – a non-singular conformal metric times an overall conformal factor \(a(\eta )\)  which momentarily passes through zero).
